A circle is defined by the equation x2 + y2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the length of the radius?

We can say that:

8x = - 2ax

8 = - 2a

a = - 4

22y = - 2by

22 = - 2b

b = - 11

37 = a² + b² - r²

37 = (-4) ² + (-11) ² - r²

r² = 16 + 121 - 37

r² = 100

r = 10

With all this information, we can say that:

The center of the circle is: (-4; - 11)

and the radius of the circle is r = 10

P. S:

(a - x) ² + (b-y) ² = r²

a² - 2ax + x² + b² - 2by + y² - r² = 0

x² + y² - 2ax - 2by + a² + b² - r² = 0